Question

triangle abc has coordinates a(2,0), b(-1,5), and c(4,3). determine the coordinates of the vertices of the image after a translation along the vector 4) oaa(2,0), b(-1,-5), and c(4,-3) ob)a(-2,0), b(1,5), and c(-4,3) oc)a(2,2), b(-1,7), and c(4,5) od)a(5,-4), b(2,1), and c(7,-1)

Explanation:

Step1: Understand translation vector

A translation along the vector \((3,-4)\) means for each point \((x,y)\), the new point \((x',y')\) is given by \(x'=x + 3\) and \(y'=y-4\).

Step2: Translate point \(A(2,0)\)

For \(A(2,0)\), \(x = 2\), \(y = 0\). Then \(x'=2 + 3=5\), \(y'=0-4=-4\). So \(A'\) is \((5,-4)\).

Step3: Translate point \(B(-1,5)\)

For \(B(-1,5)\), \(x=-1\), \(y = 5\). Then \(x'=-1+3 = 2\), \(y'=5 - 4=1\). So \(B'\) is \((2,1)\).

Step4: Translate point \(C(4,3)\)

For \(C(4,3)\), \(x = 4\), \(y = 3\). Then \(x'=4+3=7\), \(y'=3-4=-1\). So \(C'\) is \((7,-1)\).

Answer:

D. \(A'(5,-4)\), \(B'(2,1)\), and \(C'(7,-1)\)